MinT - Information on Result #1013104

Information on Result #1013104

Linear OOA(5⁹³, 2796295, F₅, 3, 11) (dual of [(2796295, 3), 8388792, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(5¹², 94, F₅, 3, 5) (dual of [(94, 3), 270, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(5¹², 95, F₅, 2, 5) (dual of [(95, 2), 178, 6]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OOA(5¹, 31, F₅, 2, 1) (dual of [(31, 2), 61, 2]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(5¹, s, F₅, 2, 1) for arbitrarily large s, using
        appending 1 arbitrary column [i] based on linear OA(5¹, s, F₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
    2. linear OOA(5³, 31, F₅, 2, 2) (dual of [(31, 2), 59, 3]-NRT-code), using
      - appending kth column [i] based on linear OA(5³, 31, F₅, 2) (dual of [31, 28, 3]-code), using
        Hamming code H(3,5) [i]
    3. linear OOA(5⁸, 33, F₅, 2, 5) (dual of [(33, 2), 58, 6]-NRT-code), using
      - extracting embedded OOA [i] based on digital (3, 8, 33)-net over F₅, using
        linear code embedding found in a computer search [i]
linear OOA(5⁸¹, 2796201, F₅, 3, 11) (dual of [(2796201, 3), 8388522, 12]-NRT-code), using
- OOA 3-folding [i] based on linear OA(5⁸¹, large, F₅, 11) (dual of [large, large−81, 12]-code), using
  - the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 5²⁰âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(5¹³³, 5592590, F₅, 3, 11) (dual of [(5592590, 3), 16777637, 12]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs